Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2 - 2}{x - 1} = \dfrac{-7x + 6}{x - 1}$
Answer: Multiply both sides by $x - 1$ $ \dfrac{x^2 - 2}{x - 1} (x - 1) = \dfrac{-7x + 6}{x - 1} (x - 1)$ $ x^2 - 2 = -7x + 6$ Subtract $-7x + 6$ from both sides: $ x^2 - 2 - (-7x + 6) = -7x + 6 - (-7x + 6)$ $ x^2 - 2 + 7x - 6 = 0$ $ x^2 - 8 + 7x = 0$ Factor the expression: $ (x - 1)(x + 8) = 0$ Therefore $x = 1$ or $x = -8$ However, the original expression is undefined when $x = 1$. Therefore, the only solution is $x = -8$.